all the same vs even so

all the same and even so both are adverbs.

Word	Noun	Adjective	Verb	Adverb
all the same	No	No	No	Yes
even so	No	No	No	Yes

As adverbs, all the same and even so are synonyms defined as:

all the same and even so: despite anything to the contrary (usually preceding a concession)

Other synonyms of all the same include at the same time, however, nevertheless, nonetheless, notwithstanding, still, withal, yet.

all the same (adverb)	even so (adverb)
despite anything to the contrary (usually preceding a concession)	despite anything to the contrary (usually preceding a concession)